Estudio de la función nuclear de DGKz I Existen datos que demuestran como

The last unknown mixing angle is θ13. The current limit on this parameter was set by the Chooz experiment [83] to be sin²2θ < 0.15 at 90 %. A non-zero value of θ13 would open up an avenue for observing leptonic CP violation. In MINOS a non-zero θ13would manifest itself as a sub-dominant oscillation of νµ→ ν_e. MINOS has observed an excess of events [18] consistent with a non-zero θ13

near the Chooz limit.

ErecoGeV NData SNC B^ν_CC^µ B^ν_CC^τ B^ν_CCn^e 0–3 141 125.1 13.3 1.4 2.3 (12.4) 3–120 247 130.4 84.0 4.9 16.0 (32.8) 0–3 R = 0.99±0.09±0.07-0.08(νe) 3–120 R = 1.09±0.12±0.10-0.13(νe) 0–120 R = 1.04±0.08±0.07-0.10(νe)

Table 6.2: Number of data events with the predicted MC events for the NC anal-ysis. The ratio of data events to prediction R are in agreement with 3 active flavours

6.3. THE MINOS CHARGED CURRENT νE ANALYSIS 101

Figure 6.4: The MINOS best fit for θ23 and θ34. Solid line and filled star are the 90 % contour and best fit point if θ₁₃ = 0^◦ and the dashed line and empty star is 90% contour and best fit point if θ13 = 12^◦ at the CHOOZ limit. a) m4 ≡ m₁. b) m₄  m₃.

6.3.1 Selecting and Classifying Events

MINOS is able to discover θ₁₃ by searching for ν_eappearance in the NuMI beam.

As with the νµ analysis, only CC interactions allow identification of the neutrino in this analysis via the identification of the e produced in ν_e + Fe → e⁻ + X. Only events with an energy between 1 GeV and 8 GeV are used in this analysis, as this is the energy range where most ν_µ disappear and thus where ν_e appearance is expected to occur due to oscillation. To select νe events cuts are made on:

• Shower – events are required to have a reconstructed shower and at least five contiguous planes with energy above an energy threshold;

• Tracks – tracks longer than 25 planes are rejected.

This increases the ratio of signal to background from 1:55 to 1:12 assuming the Chooz limit of sin²2θ₁₃. To achieve further reduction of the background, an Artifical Neural Network (ANN) with 11 parameters, that characterise the transverse and longitudinal energy deposition of events, is used. The ANN is trained with MC to separate νe-CC from NC and νµbackground events. This increases the signal to background ratio to 1:4.

Figure 6.5: Result of NC analysis with 3.18 × 10²⁰ POT [115]. The best fit point and 90 % contour for the two parameters of neutrino oscillation with decay, where αis the mass of the neutrino over lifetime

6.3.1.1 Predicting the Far Detector Spectrum

As with the NC analysis, the result of the FD prediction relies on knowing the make-up of events selected in the ND, because different ν backgrounds oscillate with different parameters. When the selection parameters were applied to ND MC and data there was a 20 – 40% discrepancy. The MC is therefore corrected in a similar way to the NC analysis. Horn-on and horn-off data were compared in the ND as these have very different backgrounds. Horn-on data is data collected with the focusing horns powered, and horn-off data is data collected when the focusing horns were switched off. In the horn-off case the low energy peak of CC events disappears so the dominant background is the feed down of higher energy NC events. The number of events in each configuration is given by the following two equations with two unknowns:

N^{(On Data)} = N^{(On data)}_NC +N^{(On Data)}_CC +N^{(On Data)}_bνe

N^{(Off Data)} = rNCN^{(On Data)}_NC +rCCN^{(On Data)}_CC +rbνeN^{(On Data)}_bνe ,

where N^{(On Data)} and N^{(Off Data)} are the total number of events selected in the ND for horn-on and horn-off respectively. N^{(On data)}_NC and N^{(On Data)}_CC are the numbers of NC and CC events selected with the horn-on data and are the unknowns. The

6.3. THE MINOS CHARGED CURRENT νE ANALYSIS 103 number of beam νe selected, N^{(On Data)}_bν

e , is taken from the weighted beam fit MC.

The r parameters are the ratios between the various component parts between horn-off and horn-on for MC. These are obtained by the following equations:

rNC = N^{(Off MC)}_NC N^{(On MC)}_NC rCC = N^{(Off MC)}_CC N^{(On MC)}_CC rbνe = N^{(Off MC)}_bνe N^{(On MC)}_bν

e

These ratios were checked by creating a CC enhanced sample of data and anti-CC background by applying the PID, from the νµ-CC analysis.

6.3.1.2 Backup Far Detector Prediction

A separate method was developed as a check for correcting the ND background.

A second set of showers were derived from ν_µ-CC events selected with the CC PID. The hits associated with the muon track were removed and the remaining shower was passed through the reconstruction software to get a clean shower sample. Both data and MC went through this process and then the νe selection was applied. The ratio of muon-removed data to muon-removed MC was used to get the relative components of the background for the νe analysis. These ratios agree those obtained with the horn-on/horn-off method. The FD prediction is then found by multiplying the component ND data by the ratio between the FD MC spectrum and ND MC spectrum. This gives a prediction at the FD for the background summed over energy to be 18.2 NC events, 5.1 νµ-CC events, 2.3 beam ν_eand 1.1 ν_τ events to give a total of 26.6 events.

To test the efficiency for selecting νe-CC events the muon-removed sample of events had an electron added, of the same momentum as the removed muon, for both MC and data. The selection efficiency was found to be 41.4±1.4 %.

6.3.2 Charged Current ν

Systematic Errors

Systematic errors were worked out by generating modified MC samples and quantifying the change in the background events on the FD prediction. Table

Uncertainty source Uncertainty on background events (%)

i)Far/Near ratio: 6.4

a)Relative energy scale 3.1

b)PMT gains 2.7

c)PMT crosstalk 2.2

d)Relative event rate 2.4

e)All others 3.7

ii)Horn off (systematic) 2.7

iii)Horn off (statistical) 2.3

Total Systematic (sum in quadrature) 7.3

Expected Statistical Uncertainty 19

Table 6.3: Breakdown of the percentage change in background in the FD predic-tion for the νe-CC analysis.

6.3 shows the most important errors that arise from the F/N method, as well as the error from the horn-off method of determining the background. Together they give a systematic uncertainty of 7.3 % on the number of background events. The statistical error is 19 %.

The Far/Near ratio error is made up from multiple sources the most important are a) relative energy scale calibration errors, b) and c) details of the modelling of the photomultiplier gains and crosstalk, d) relative event normalisation.

6.3.3 ν

Results

The FD data was unblinded in two steps. First the data that passed all cuts ex-cept the ANN cut were unblinded. There were 146 data events below the ANN cut of 0.55 compared to the prediction of 132⁺¹²₋₁₂(stat.)⁺⁸₋₈(syst.). After checks on this sample had been completed the signal region was investigated above ANN = 0.7. In this region there were 35 events compared to the prediction of 27⁺⁵₋₅(stat.)⁺²₋₂(syst.).

A second selection method, Library Event Matching (LEM), was chosen as

6.3. THE MINOS CHARGED CURRENT νE ANALYSIS 105

Figure 6.6: TThe MINOS FD ANN spectrum with the best fit oscillation and the best confidence levels for normal and inverse hierarchy. a) Distribution of events for the ANN PID. Black points are data with statistical errors and the red line is prediction. b) values of sin²2θ₁₃ and δCP the data are consistent with for normal (top) and inverse (bottom) hierarchy.

a back-up. In the LEM method the data events are compared to a library of MC events. A PID is created from three variables: fraction of 50 best matches that are ν_e CC; mean y of 50 matches that are νeCC; mean Qfrac of best 50 matches that are νe CC, where Qfrac = _Q ^Qmatched

matchedQunmatched. These three parameters are combined into an energy-binned likelihood. The LEM gives a better background rejection and gives a prediction of 22⁺⁵₋₅(stat.)⁺³₋₃(syst.). The number of data events selected were 28, which, like the ANN selection, is less than a 2σ excess.

Taking the ANN excess and taking |∆m²| = 2.43× 10⁻³eV² and sin²2θ₂₃= 1.0, the best fit in normal hierarchy is just below the Chooz limit for full three flavour neutrino oscillation see figure 6.6.